Adaptive Image Contrast Enhancement by Computing Distances into a 4-Dimensional Fuzzy Unit Hypercube

A new fuzzy procedure for adaptive gray-level image contrast enhancement (CE) is presented in this paper. Starting from the pixels belonging to a normalized gray-level image, an appropriate smooth S-shaped fuzzy membership function (MF) is considered for gray-scale transformation and is adaptively developed through noise reduction and information loss minimization. Then, a set of fuzzy patches is extracted from the MF, and for each support of each patch, we compute four ascending-order statistics that become points inside a 4-D fuzzy unit hypercube after a suitable fuzzification step. CE is performed by computing the distances among the above points and the points of maximum darkness and maximum brightness (special vertexes in the hypercube), and by determining the rotation of the tangent line to the MF around a crucial point where fuzzy patches and the MF coexist. The proposed procedure enables high CE in all the treated images with performance that is fully comparable with that obtained by three more sophisticated fuzzy techniques and by standard histogram equalization.

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